Flow in Rectangular Geometries

Note that Q = AuWH. If there is symmetry about x = 0 and y = 0, then 

The convective diffusion equation for flow in rectangular ducts is 

The associated boundary conditions are zero slope at the walls and at any planes of symmetry. The counterpart of Equation 16.3 for the convective diffusion of heat is 

The boundary conditions are specified temperatures or zero slope at the walls and zero slope at any planes of symmetry. Compare Equations 8.20 and 8.24. The major difference is that is now a function of x and y rather than just r. Compare also Equations 8.50 and 8.51. Elows in the cross-channel directions that correspond to Vr have been ignored because cross-channel diffusion in microscale devices will largely eliminate the concentration and temperature gradients that drive these flows. 

The velocity profile V ix, y) must be determined. Suppose IT/// 1 so that side-wall effects at x = 1T can be ignored. This limiting case is known as slit flow or flow between parallel plates. The velocity profile within the slit is 

---